piecewise linear approximation

["msimon"]

If a function f(x) in C^2(0,1) is approximated by a piecewise linear
polynomial, how do I find a bound on the error?

For a specific interval [x(j), x(j+1)], I know:

p(x) = [f(x(j+1)) - f(x(j))] x / h_j + f(x(j))

f(x) - p(x) = f(x) - [f(x(j+1)) - f(x(j))] x / h_j - f(x(j))

where to go from here?